Physical modeling of ribosomes along messenger RNA: Estimating kinetic parameters from ribosome profiling experiments using a ballistic model.

Gene expression is the synthesis of proteins from the information encoded on DNA. One of the two main steps of gene expression is the translation of messenger RNA (mRNA) into polypeptide sequences of amino acids. Here, by taking into account mRNA degradation, we model the motion of ribosomes along mRNA with a ballistic model where particles advance along a filament without excluded volume interactions. Unidirectional models of transport have previously been used to fit the average density of ribosomes obtained by the experimental ribo-sequencing (Ribo-seq) technique in order to obtain the kinetic rates. The degradation rate is not, however, accounted for and experimental data from different experiments are needed to have enough parameters for the fit. Here, we propose an entirely novel experimental setup and theoretical framework consisting in splitting the mRNAs into categories depending on the number of ribosomes from one to four. We solve analytically the ballistic model for a fixed number of ribosomes per mRNA, study the different regimes of degradation, and propose a criterion for the quality of the inverse fit. The proposed method provides a high sensitivity to the mRNA degradation rate. The additional equations coming from using the monosome (single ribosome) and polysome (arbitrary number) ribo-seq profiles enable us to determine all the kinetic rates in terms of the experimentally accessible mRNA degradation rate.

Supercoiled DNA and non-equilibrium formation of protein complexes: A quantitative model of the nucleoprotein ParBS partition complex.

ParABS, the most widespread bacterial DNA segregation system, is composed of a centromeric sequence, parS, and two proteins, the ParA ATPase and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS-anchored complexes that serve as substrates for ParA molecules to catalyze positioning and segregation events. The exact nature of this ParBS complex has remained elusive, what we address here by revisiting the Stochastic Binding model (SBM) introduced to explain the non-specific binding profile of ParB in the vicinity of parS. In the SBM, DNA loops stochastically bring loci inside a sharp cluster of ParB. However, previous SBM versions did not include the negative supercoiling of bacterial DNA, leading to use unphysically small DNA persistences to explain the ParB binding profiles. In addition, recent super-resolution microscopy experiments have revealed a ParB cluster that is significantly smaller than previous estimations and suggest that it results from a liquid-liquid like phase separation. Here, by simulating the folding of long (≥ 30 kb) supercoiled DNA molecules calibrated with realistic DNA parameters and by considering different possibilities for the physics of the ParB cluster assembly, we show that the SBM can quantitatively explain the ChIP-seq ParB binding profiles without any fitting parameter, aside from the supercoiling density of DNA, which, remarkably, is in accord with independent measurements. We also predict that ParB assembly results from a non-equilibrium, stationary balance between an influx of produced proteins and an outflux of excess proteins, i.e., ParB clusters behave like liquid-like protein condensates with unconventional "leaky" boundaries.

Modelling the effect of ribosome mobility on the rate of protein synthesis.

Translation is one of the main steps in the synthesis of proteins. It consists of ribosomes that translate sequences of nucleotides encoded on mRNA into polypeptide sequences of amino acids. Ribosomes bound to mRNA move unidirectionally, while unbound ribosomes diffuse in the cytoplasm. It has been hypothesized that finite diffusion of ribosomes plays an important role in ribosome recycling and that mRNA circularization enhances the efficiency of translation, see e.g. Lodish et al. (Molecular cell biology, 8th edn, W.H. Freeman and Company, San Francisco, 2016). In order to estimate the effect of cytoplasmic diffusion on the rate of translation, we consider a totally asymmetric simple exclusion process coupled to a finite diffusive reservoir, which we call the ribosome transport model with diffusion. In this model, we derive an analytical expression for the rate of protein synthesis as a function of the diffusion constant of ribosomes, which is corroborated with results from continuous-time Monte Carlo simulations. Using a wide range of biological relevant parameters, we conclude that diffusion is not a rate limiting factor in translation initiation because diffusion is fast enough in biological cells.

Physical Modeling of a Sliding Clamp Mechanism for the Spreading of ParB at Short Genomic Distance from Bacterial Centromere Sites.

Bacterial ParB partitioning proteins involved in chromosomes and low-copy-number plasmid segregation are cytosine triphosphate (CTP)-dependent molecular switches. CTP-binding converts ParB dimers to DNA clamps, allowing unidimensional diffusion along the DNA. This sliding property has been proposed to explain the ParB spreading over large distances from parS centromere sites where ParB is specifically loaded. We modeled such a "clamping and sliding" mechanism as a typical reaction-diffusion system, compared it to the F plasmid ParB DNA binding pattern, and found that it can account neither for the long range of ParB binding to DNA nor for the rapid assembly kinetics observed in vivo after parS duplication. Also, it predicts a strong effect on the F plasmid ParB binding pattern from the presence of a roadblock that is not observed in ChIP-sequencing (ChIP-seq). We conclude that although "clamping and sliding" can occur at short distances from parS, another mechanism must apply for ParB recruitment at larger genomic distances.

A conserved mechanism drives partition complex assembly on bacterial chromosomes and plasmids.

Chromosome and plasmid segregation in bacteria are mostly driven by ParABS systems. These DNA partitioning machineries rely on large nucleoprotein complexes assembled on centromere sites (parS). However, the mechanism of how a few parS-bound ParB proteins nucleate the formation of highly concentrated ParB clusters remains unclear despite several proposed physico-mathematical models. We discriminated between these different models by varying some key parameters in vivo using the F plasmid partition system. We found that "Nucleation & caging" is the only coherent model recapitulating in vivo data. We also showed that the stochastic self-assembly of partition complexes (i) is a robust mechanism, (ii) does not directly involve ParA ATPase, (iii) results in a dynamic structure of discrete size independent of ParB concentration, and (iv) is not perturbed by active transcription but is by protein complexes. We refined the "Nucleation & caging" model and successfully applied it to the chromosomally encoded Par system of Vibrio cholerae, indicating that this stochastic self-assembly mechanism is widely conserved from plasmids to chromosomes.